Cutting the Cross

After solving the cutting the cross problem (link: http://www.mathsisfun.com/puzzles/cutting-across-a-cross.html), I began to wonder: is there a formula to determine the maximum of parts based on the number of cuts of a corss?

I feel as though this has some relation to the lazy caterer's problem. (link:http://en.wikipedia.org/wiki/Lazy_caterer%27s_sequence)